Divergence Index (10/40/1.0, squared deviation)
The distance between two moving averages measures how far price has strayed from its own equilibrium, but that distance means different things in calm and in agitated markets. Dividing it by volatility and comparing it against bands that also adjust yields a departure that is comparable over time — and an extreme departure against the trend is a chance to enter with the trend, not a reversal signal.
Measured in crypto — Binance spot · 540 pairs, delisted ones included · 0.2% per round trip
- ✓invariance
- ?costs
- ✗placebo
- ✗benchmark
- ?out of sample
- ?multiple testing
At its worst the account was worth 100% less than its own best previous moment, and it spent 2,821 days below that peak.
What was measured
How many of those trades actually count
What it paid, before any deductions
Why it did not pass — it died here · against randomly drawn dates
What would have happened to the money
The account would not fit every signal
What this result does NOT say
- One market, one universe
- Measured on 512 spot cryptocurrency pairs, delisted ones included. It says nothing about futures, equities or indices, nor about how the same technique behaves in another market.
- One window of time, not every window
- The measured period runs from 2017-08-17 to 2026-07-28. A market moves through regimes, and a technique can work in one and fail in another — the card measures the regimes that fit inside this window, not the ones still to come.
- One cost structure
- The cost charged is 0.10% per leg, in and out. Anyone paying more than that gets a worse result, and anyone paying less gets a better one — the verdict holds for this fee.
- One exit rule
- The trade was closed by: the technique itself (held until the opposite signal). The same entry measured with a different exit is a different strategy, and can earn a different verdict — it happens in this archive.
- The number of trades is not the sample size
- There are 2,757 trades, but only 127 independent market episodes: a single move fires the technique across dozens of assets at once, and counting those as separate observations inflates any result. It is the smaller number that governs the arithmetic. With 127 episodes, what the data supports is a range from -11.14% to +2.97% per trade — the published average is the centre of it, not the exact measurement.
- Daily bars
- Measured at the daily close. Nothing here measures what happens inside the day, and an intraday technique is not auditable with this data.
Numbers and reproducibility
The six controls
| control | status | t | threshold | episodes |
|---|---|---|---|---|
| invariance | passed | — | — | — |
| costs | inconclusive | -1.20 | 1.98 | 127 |
| placebo | failed | -1.21 | 1.98 | 127 |
| benchmark | failed | — | — | — |
| out of sample | inconclusive | — | — | — |
| multiple testing | inconclusive | — | — | — |
- invariance2757 signals across 750934 barsconcentration: +25.57% of the profit sits in the top 5% of trades — with the dates shuffled, +42.18% (fails above +50.00%)
- costsgross -4.084% · cost 0.200% · net -4.284% (t=-1.20) · the range reaches +2.774%
- placeboactual -4.284% · placebo +0.056% · excess -4.341% ± 3.598% (t=-1.21 against a threshold of 1.98, 127 real groups, 137,850 sham dates, draw error ±0.104%)
- benchmarktechnique -4.28% · buy and hold (same horizon) +1.83% · excess -6.12%
- out of sampleasset half A: -2.416% (t=-1.04, 121 episodes) · asset half B: -6.138% (t=-1.18, 115 episodes) · liquid half (>= US$ 2,107,235/day): -3.212% (t=-0.66, 121 episodes) · illiquid half: -5.392% (t=-1.38, 111 episodes) · period 1/4 (2018-03-17 a 2022-06-14): -16.845% (t=-2.37, 62 episodes) · period 2/4 (2022-06-20 a 2023-08-07): -1.068% (t=-0.51, 19 episodes) · period 3/4 (2023-08-08 a 2025-04-27): -2.967% (t=-1.15, 28 episodes) · period 4/4 (2025-04-28 a 2026-07-15): +3.455% (t=2.17, 20 episodes)
- multiple testing2 variation(s) tested · t=-1.20 across 127 episodes (equivalent to t=-1.19) · p≈0.2342 · false positives expected by chance ≈ 0.47
Equity — outside the six controls, and here is why
The t of the trade series is invariant to bet size: 0.5%, 1% and 3% agree to the sixth decimal. Nothing here moves the verdict — it moves what the account would have lived through.
- risking 1.0% per trade
- ×0.00
- worst drawdown from the peak
- −100%
- days below the previous peak
- 2,821
- signals refused for lack of capital
- 91%
- paths where the account halved (out of 12)
- 12
Reproducibility
- period
- 2017-08-17 to 2026-07-28
- assets that traded
- 512
- variations tested before this one
- 2
- gross per trade
- −4.08%
- net per trade
- −4.28%
- exit rule
- the technique itself (held until the opposite signal)
- median duration bars
- 23
- mean duration bars
- 29.9
- max duration bars
- 203
- fee per leg
- 0.001
- episode days
- 23
- seed
- 20260728
- DI fast
- 10
- DI slow
- 40
- DI factor
- 1.0
- DI squared
- 1.0
Binance spot klines (delisted pairs included) · collected from 2026-07-27 23:31 to 2026-08-03 10:49 · 540 assets · 750,934 bars · 2017-08-17 to 2026-07-28
Hypothesis, filed before the result
Difference between the 10- and 40-day averages, divided by the standard deviation of daily changes — a volatility adjustment. Bands at ±1.0 deviation of the index itself. The rule says 'buy when the index falls below the lower band WHILE IN AN UPTREND', and the source does NOT define the trend. The step is named and not defined; we will adopt the direction of the slow average and that goes declared as the auditor's choice. And there is an ambiguity in the printed formula: it is not clear whether the standard deviation enters squared. Both readings will be measured. Family prediction, filed before measuring: (1) the control that kills the most will be COST, and not invariance — unlike the `adaptativos` family, because these are discrete-signal oscillators, they turn over less and are not always in the market; (2) the DIVERGENCE techniques will come out mostly INCONCLUSIVE, because they require two aligned peaks and fire rarely; (3) none survives the family's Benjamini-Hochberg. I record that prediction (1) is the opposite of the one I made in `adaptativos` and that was confirmed there — if I get it wrong again in the same direction, that is a sign I am misreading the mechanism of cost, not the technique.
filed on 2026-07-31, before the number existed
The original, as it was filed
Diferença entre médias de 10 e 40 dias, dividida pelo desvio padrão das variações diárias — ajuste de volatilidade. Bandas em ±1,0 desvio do próprio índice. ⚠️ A regra diz 'compre quando o índice cai abaixo da banda inferior ESTANDO EM TENDÊNCIA DE ALTA', e a fonte NÃO define a tendência. O passo é nomeado e não definido; adotaremos a direção da média lenta e isso vai declarado como escolha do auditor. ⚠️ E há ambiguidade na fórmula impressa: não fica claro se o desvio padrão entra ao quadrado. As duas leituras serão medidas. Previsão da família, registrada antes de medir: (1) o controle que mais mata será o CUSTO, e não o invariante — diferente da família `adaptativos`, porque estes são osciladores de sinal discreto, giram menos e não são sempre-no-mercado; (2) as técnicas de DIVERGÊNCIA sairão majoritariamente INCONCLUSIVAS, porque exigem dois picos alinhados e disparam pouco; (3) nenhuma sobrevive ao Benjamini-Hochberg da família. ⚠️ Registro que a previsão (1) é o oposto da que fiz em `adaptativos` e que se confirmou lá — se eu errar de novo na mesma direção, é sinal de que estou lendo mal o mecanismo do custo, e não a técnica.
Pre-registration exists to keep prediction apart from rationalisation: written after the number, every hypothesis is right.